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transport density

ESAIM: Control, Optimisation and Calculus of Variations (1)

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Sharp summability for Monge Transport densityvia Interpolation
Luigi De Pascale, Aldo Pratelli
Journal:

ESAIM: Control, Optimisation and Calculus of Variations / Volume 10 / Issue 4 / October 2004

Published online by Cambridge University Press:

15 October 2004, pp. 549-552

Print publication:

October 2004
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Using some results proved in De Pascale and Pratelli [Calc. Var. Partial Differ. Equ.14 (2002) 249-274] (and De Pascale et al. [Bull. London Math. Soc.36 (2004) 383-395]) and a suitable interpolation technique, we show that the transport density relative to an Lp source is also an Lp function for any $1\leq p\leq +\infty$ .